Tobias Hilgart

activity

20212026

most citedOn a family of cubic Thue Equations involving Fibonacci and Lucas numbers

2 citations · 2 across the 8 of their papers we have counts for

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math.NT2024

On the unique solvability of the simultaneous Pell equations $x^{2} - a y^{2} = 1$ and $z^{2} - b x^{2} = 1$

Tobias Hilgart, Volker Ziegler

We consider the simultaneous Pell equations $x^{2} - a y^{2} = 1, z^{2} - b x^{2} = 1,$ where $a > b \geq 2$ are positive integers. We describe a procedure which, for any fixed $b$ ,…

math.NT2024

On split families of Thue equations with linear recurrence sequences as factors

Tobias Hilgart

We consider a parametrised family of Thue equations, \[ (x-G_1(n)\, y) \cdots (x-G_d(n)\, y) - y^d = \pm 1, \] which was first considered by Thomas to have an explicit set of solut…

math.NT2024

On a conjecture of Levesque and Waldschmidt II

Tobias Hilgart, Volker Ziegler

Related to Shank's notion of simplest cubic fields, the family of parametrised Diophantine equations, \[ x^3 - (n-1) x^2 y - (n+2) xy^2 - 1 = \left( x - λ_0 y\right) \left(x-λ_1 y\…

On the unique solvability of the simultaneous Pell equations x2−ay2=1 and z2−bx2=1

On split families of Thue equations with linear recurrence sequences as factors

On a conjecture of Levesque and Waldschmidt II

On the unique solvability of the simultaneous Pell equations $x^{2} - a y^{2} = 1$ and $z^{2} - b x^{2} = 1$